check items
The first two plausible problems that come to mind are:
1.) Dead spot in motor windings. If motor is truly humming and NOT turning under load. I had this happen once and had to have the motor rewound.
2.) Broken belt, loose belt or belt slipped off pulley (often cause by stretached belt.) In these cases the motor is rotating but not able to trasmit torque to tub via belt.
I recomment that you take back off and see if motor is turning or stalled and just humming when timer is in wash mode.
If motor is not turning, replace or have rewound. A dead spot in the field windings will prevent the motor from turning under heavy load. However, sometimes it can still give enough pull to allow motor to do light tasks, such as draining. that is the way mine was.
If motor is turning, then the belt is stretched and not transmitting power, or it is broken or it has slipped off pulley.
If brokent, you can likely find belt on Ebay or Sears Parts Direct. If it has slipped off the pulley, cut off power and replace onto pulleys. Keep in mind it may have come off due to it being stretched and will most likely come off again sometime in the near future, so best to replace.